New equations for the dynamics of a two-phase mixture are derived in a companion paper <Bercovici et al., this issue (a)>. These equations do not invoke a bulk viscosity as most previous papers have done, and use the existence of the pressure difference between the two phases, including the possibility of surface energy at the interface between the phases. In this paper we show how a two-phase mixture reacts to simple stress fields. As a basic example, we discuss the deformation of a porous material confined by an impermeable jacket and loaded by a porous piston and show that the fluid can never be totally extracted from the matrix. We demonstrate that an unconfined porous sample is stronger under shear deformation than under normal stress. We consider spherically symmetric compaction and show that some unphysical results obtained using a constant matrix bulk viscosity are naturally avoided in our approach. We discuss the problem of compaction of a two-phase liquid in the presence of surface tension. In a one-dimensional simulation the surface tension generates porosity instabilities that tend to localize the fluid into narrow sills and dikes that cannot reach the surface. ¿ 2001 American Geophysical Union